





'''simple docstring'''


import os
import sys
import tempfile

import torch

from .state import AcceleratorState
from .utils import PrecisionType, PrepareForLaunch, is_mps_available, patch_environment


def 						__a(SCREAMING_SNAKE_CASE_	:       List[Any]		,							SCREAMING_SNAKE_CASE_	:       Optional[int]=()		,							SCREAMING_SNAKE_CASE_	:       Optional[int]=None		,							SCREAMING_SNAKE_CASE_	:       Optional[Any]="no"		,							SCREAMING_SNAKE_CASE_	:       Any="29500"     ):



    '''simple docstring'''





    _lowerCAmelCase						      =   False
    _lowerCAmelCase						      =   False
    if any(key.startswith("KAGGLE"     ) for key in os.environ.keys()     ):
        _lowerCAmelCase						      =   True
    elif "IPython" in sys.modules:
        _lowerCAmelCase						      =   "google.colab" in str(sys.modules["IPython"].get_ipython()     )

    try:
        _lowerCAmelCase						      =   PrecisionType(mixed_precision.lower()     )
    except ValueError:
        raise ValueError(
            F'''Unknown mixed_precision mode: {args.mixed_precision.lower()}. Choose between {PrecisionType.list()}.'''     )

    if (in_colab or in_kaggle) and (os.environ.get("TPU_NAME"		,							SCREAMING_SNAKE_CASE_     ) is not None):
        # TPU launch
        import torch_xla.distributed.xla_multiprocessing as xmp

        if len(AcceleratorState._shared_state     ) > 0:
            raise ValueError(
                "To train on TPU in Colab or Kaggle Kernel, the `Accelerator` should only be initialized inside "
                "your training function. Restart your notebook and make sure no cells initializes an "
                "`Accelerator`."     )
        if num_processes is None:
            _lowerCAmelCase						      =   8

        _lowerCAmelCase						      =   PrepareForLaunch(SCREAMING_SNAKE_CASE_		,							distributed_type="TPU"     )
        print(F'''Launching a training on {num_processes} TPU cores.'''     )
        xmp.spawn(SCREAMING_SNAKE_CASE_		,							args=SCREAMING_SNAKE_CASE_		,							nprocs=SCREAMING_SNAKE_CASE_		,							start_method="fork"     )
    elif in_colab:
        # No need for a distributed launch otherwise as it's either CPU or one GPU.
        if torch.cuda.is_available():
            print("Launching training on one GPU."     )
        else:
            print("Launching training on one CPU."     )
        function(*SCREAMING_SNAKE_CASE_     )
    else:
        if num_processes is None:
            raise ValueError(
                "You have to specify the number of GPUs you would like to use, add `num_processes=...` to your call."     )

        if num_processes > 1:
            # Multi-GPU launch
            from torch.multiprocessing import start_processes
            from torch.multiprocessing.spawn import ProcessRaisedException

            if len(AcceleratorState._shared_state     ) > 0:
                raise ValueError(
                    "To launch a multi-GPU training from your notebook, the `Accelerator` should only be initialized "
                    "inside your training function. Restart your notebook and make sure no cells initializes an "
                    "`Accelerator`."     )

            if torch.cuda.is_initialized():
                raise ValueError(
                    "To launch a multi-GPU training from your notebook, you need to avoid running any instruction "
                    "using `torch.cuda` in any cell. Restart your notebook and make sure no cells use any CUDA "
                    "function."     )

            # torch.distributed will expect a few environment variable to be here. We set the ones common to each
            # process here (the other ones will be set be the launcher).
            with patch_environment(
                world_size=SCREAMING_SNAKE_CASE_		,							master_addr="127.0.01"		,							master_port=SCREAMING_SNAKE_CASE_		,							mixed_precision=SCREAMING_SNAKE_CASE_     ):
                _lowerCAmelCase						      =   PrepareForLaunch(SCREAMING_SNAKE_CASE_		,							distributed_type="MULTI_GPU"     )
                print(F'''Launching training on {num_processes} GPUs.'''     )
                try:
                    start_processes(SCREAMING_SNAKE_CASE_		,							args=SCREAMING_SNAKE_CASE_		,							nprocs=SCREAMING_SNAKE_CASE_		,							start_method="fork"     )
                except ProcessRaisedException as e:
                    if "Cannot re-initialize CUDA in forked subprocess" in e.args[0]:
                        raise RuntimeError(
                            "CUDA has been initialized before the `notebook_launcher` could create a forked subprocess. "
                            "This likely stems from an outside import causing issues once the `notebook_launcher()` is called. "
                            "Please review your imports and test them when running the `notebook_launcher()` to identify "
                            "which one is problematic."     ) from e

        else:
            # No need for a distributed launch otherwise as it's either CPU, GPU or MPS.
            if is_mps_available():
                _lowerCAmelCase						      =   "1"
                print("Launching training on MPS."     )
            elif torch.cuda.is_available():
                print("Launching training on one GPU."     )
            else:
                print("Launching training on CPU."     )
            function(*SCREAMING_SNAKE_CASE_     )





def 						__a(SCREAMING_SNAKE_CASE_	:       List[str]		,							SCREAMING_SNAKE_CASE_	:       Optional[int]=()		,							SCREAMING_SNAKE_CASE_	:       List[str]=2     ):



    '''simple docstring'''





    from torch.multiprocessing import start_processes

    with tempfile.NamedTemporaryFile() as tmp_file:
        # torch.distributed will expect a few environment variable to be here. We set the ones common to each
        # process here (the other ones will be set be the launcher).
        with patch_environment(
            world_size=SCREAMING_SNAKE_CASE_		,							master_addr="127.0.01"		,							master_port="29500"		,							accelerate_mixed_precision="no"		,							accelerate_debug_rdv_file=tmp_file.name		,							accelerate_use_cpu="yes"		,							):
            _lowerCAmelCase						      =   PrepareForLaunch(SCREAMING_SNAKE_CASE_		,							debug=SCREAMING_SNAKE_CASE_     )
            start_processes(SCREAMING_SNAKE_CASE_		,							args=SCREAMING_SNAKE_CASE_		,							nprocs=SCREAMING_SNAKE_CASE_		,							start_method="fork"     )





from math import factorial







class 					__lowercase  :





							"""simple docstring"""

							def __init__(					self    ,						__UpperCAmelCase    ,						__UpperCAmelCase						)		->       Optional[int]:
														A      :					Union[str, Any]      		=					real
														if isinstance(__UpperCAmelCase    ,						__UpperCAmelCase						):
																					A      :					str      		=					[1] * rank
														else:
																					A      :					Dict      		=					rank




							def __repr__(					self						)		->       List[str]:
														return (
														    f'{self.real}+'
														    f'{"+".join(str(__UpperCAmelCase						)+"E"+str(n+1						)for n,dual in enumerate(self.duals						)						)}'
														)




							def       snake_case			(					self						)		->       Union[str, Any]:
														A      :					List[Any]      		=					self.duals.copy()
														while cur[-1] == 0:
																					cur.pop(-1						)
														return Dual(self.real    ,						__UpperCAmelCase						)




							def __add__(					self    ,						__UpperCAmelCase						)		->       Any:
														if not isinstance(__UpperCAmelCase    ,						__UpperCAmelCase						):
																					return Dual(self.real + other    ,						self.duals						)
														A      :					int      		=					self.duals.copy()
														A      :					Any      		=					other.duals.copy()
														if len(__UpperCAmelCase						) > len(__UpperCAmelCase						):
																					o_dual.extend([1] * (len(__UpperCAmelCase						) - len(__UpperCAmelCase						))						)
														elif len(__UpperCAmelCase						) < len(__UpperCAmelCase						):
																					s_dual.extend([1] * (len(__UpperCAmelCase						) - len(__UpperCAmelCase						))						)
														A      :					List[str]      		=					[]
														for i in range(len(__UpperCAmelCase						)						):
																					new_duals.append(s_dual[i] + o_dual[i]						)
														return Dual(self.real + other.real    ,						__UpperCAmelCase						)

							UpperCAmelCase_						:		int								=	__add__




							def __sub__(					self    ,						__UpperCAmelCase						)		->       List[str]:
														return self + other * -1




							def __mul__(					self    ,						__UpperCAmelCase						)		->       List[str]:
														if not isinstance(__UpperCAmelCase    ,						__UpperCAmelCase						):
																					A      :					Union[str, Any]      		=					[]
																					for i in self.duals:
																												new_duals.append(i * other						)
																					return Dual(self.real * other    ,						__UpperCAmelCase						)
														A      :					Optional[Any]      		=					[0] * (len(self.duals						) + len(other.duals						) + 1)
														for i, item in enumerate(self.duals						):
																					for j, jtem in enumerate(other.duals						):
																												new_duals[i + j + 1] += item * jtem
														for k in range(len(self.duals						)						):
																					new_duals[k] += self.duals[k] * other.real
														for index in range(len(other.duals						)						):
																					new_duals[index] += other.duals[index] * self.real
														return Dual(self.real * other.real    ,						__UpperCAmelCase						)

							UpperCAmelCase_						:		int								=	__mul__




							def __truediv__(					self    ,						__UpperCAmelCase						)		->       Optional[int]:
														if not isinstance(__UpperCAmelCase    ,						__UpperCAmelCase						):
																					A      :					Optional[Any]      		=					[]
																					for i in self.duals:
																												new_duals.append(i / other						)
																					return Dual(self.real / other    ,						__UpperCAmelCase						)
														raise ValueError




							def __floordiv__(					self    ,						__UpperCAmelCase						)		->       Union[str, Any]:
														if not isinstance(__UpperCAmelCase    ,						__UpperCAmelCase						):
																					A      :					List[Any]      		=					[]
																					for i in self.duals:
																												new_duals.append(i // other						)
																					return Dual(self.real // other    ,						__UpperCAmelCase						)
														raise ValueError






							def __pow__(					self    ,						__UpperCAmelCase						)		->       Any:
														if n < 0 or isinstance(__UpperCAmelCase    ,						__UpperCAmelCase						):
																					raise ValueError('''power must be a positive integer'''						)
														if n == 0:
																					return 1
														if n == 1:
																					return self
														A      :					Dict      		=					self
														for _ in range(n - 1						):
																					x *= self
														return x






def        snake_case__		(    lowerCamelCase_     ,				lowerCamelCase_     ,				lowerCamelCase_		):
							if not callable(lowerCamelCase_		):
														raise ValueError('''differentiate() requires a function as input for func'''		)
							if not isinstance(lowerCamelCase_     ,				(float, int)		):
														raise ValueError('''differentiate() requires a float as input for position'''		)
							if not isinstance(lowerCamelCase_     ,				lowerCamelCase_		):
														raise ValueError('''differentiate() requires an int as input for order'''		)
							A      :					Any      		=					Dual(lowerCamelCase_     ,				1		)
							A      :					Dict      		=					func(lowerCamelCase_		)
							if order == 0:
														return result.real
							return result.duals[order - 1] * factorial(lowerCamelCase_		)


if __name__ == "__main__":
		import doctest

		doctest.testmod()






		def        snake_case__		(    lowerCamelCase_		):
									return y**2 * y**4

		print(differentiate(f, 9, 2))






